Jiri Fridrich

Symmetric Ciphers Based on Two-Dimensional Chaotic Maps

In this paper, methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. Although the discretized map is a permutation and thus cannot be chaotic, it shares certain properties with its continuous counterpart as long as the number of iterations remains small. The discretized map is further extended to three dimensions and composed with a simple diffusion mechanism. As a result, a symmetric block product encryption scheme is obtained. To encrypt an N×N image, the ciphering map is iteratively applied to the image. The construction of the cipher and its security is explained with the two-dimensional Baker map. It is shown that the permutations induced by the Baker map behave as typical random permutations. Computer simulations indicate that the cipher has g...

Robust hash functions for digital watermarking

Digital watermarks have been proposed for authentication of both video data and still images and for integrity verification of visual multimedia. In such applications, the watermark has to depend on a secret key and on the original image. It is important that the dependence on the key be sensitive, while the dependence on the image be continuous (robust). Both requirements can be satisfied using special image digest functions that return the same bit-string for a whole class of images derived from an original image using common processing operations. It is further required that two completely different images produce completely different bit-strings. We discuss methods how such robust hash functions can be built. We also show how the hash bits has another application, the robust image digest can be used as a search index for an efficient image database search.

Image watermarking for tamper detection

We propose an oblivious watermarking technique for tamper detection in digital images. By comparing correlation values from different portions of the image, the technique enables us to distinguish malicious changes, such as replacing/adding features from nonmalicious changes resulting from common image processing operations. The technique can be implemented with small memory and computational requirements, which makes it potentially useful for hardware implementation in digital cameras. The technique works by dividing an image into blocks and watermarking each block with a transparent, robust watermark that sensitively depends on a secret key (cameras ID) and continuously on the image. The watermarking method is a frequency based spread spectrum technique. To achieve a continuous dependency on the image, we propose a special bit extraction procedure that extracts bits from each block by thresholding projections onto key-dependent random smooth patterns. Those bits are then used for initializing a PRNG and synthesizing the spread spectrum signal.

Images with self-correcting capabilities

In this paper, we introduce two techniques for self-embedding an image in itself as a means for protecting the image content. After self-embedding, it is possible to recover portions of the image that have been cropped out, replaced, damaged, or otherwise tampered without accessing the original image. The first method is based on transforming small 8/spl times/8 blocks using a DCT, quantizing the coefficients, and carefully encoding them in the least significant bits of other, distant squares. This method provides very high quality of reconstruction but it is very fragile. The quality of the reconstructed image areas is roughly equivalent to a 50% quality JPEG compressed original. The second method uses a principle similar to differential encoding to embed a circular shift of the original image with decreased color depth into the original image. The quality of the reconstructed image gradually degrades with increasing amount of noise in the tampered image. The first technique can also be used as a fragile watermark for image authentication, while the second technique can be classified as a semi-robust watermark.

Invertible authentication watermark for JPEG images

We present two new invertible watermarking methods for authentication of digital images in the JPEG format. While virtually all previous authentication watermarking schemes introduced some small amount of non-invertible distortion in the image, the new methods are invertible in the sense that, if the image is deemed authentic, the distortion due to authentication can be completely removed to obtain the original image data. The first technique is based on lossless compression of biased bit-streams derived from the quantized JPEG coefficients. The second technique modifies the quantization matrix to enable lossless embedding of one bit per DCT coefficient. Both techniques are fast and can be used for general distortion-free (invertible) data embedding. The new methods provide new information assurance tools for integrity protection of sensitive imagery, such as medical images or high-importance military images viewed under non-standard conditions when usual criteria for visibility do not apply.

Robust bit extraction from images

We describe an algorithm for robust extraction of bits from image blocks and a method for synthesizing a Gaussian pseudo-random sequence from those bits. The bits are extracted by thresholding projections onto random smooth patterns generated from a user-specified key. The extracted bits are further utilized to synthesize a Gaussian pseudo-random sequence that changes continuously with the image block yet depends sensitively on the secret key. The proposed technique is quite general and can be combined with the majority of oblivious watermarking schemes that generate watermarks from pseudo-random sequences. We anticipate that this algorithm will find applications in many oblivious watermarking schemes including secure data embedding into videos and watermarking images for tamper detection.

Secure Steganographic Methods for Palette Images

In this paper, we study non-adaptive and adaptive steganographic techniques for images with low number of colors in palette image formats. We have introduced the concept of optimal parity assignment for the color palette and designed an efficient algorithm that finds the optimal parity assignment. The optimal parity is independent of the image histogram and depends only on the image palette. Thus, it can be used for increasing the security of steganographic techniques that embed message bits into the parity of palette colors. We have further developed two adaptive steganographic methods designed to avoid areas of uniform color and embed message bits into texturerich portions of the cover image. Both techniques were tested on computer generated images with large areas of uniform color and with fonts on uniform background. No obvious artifacts were introduced by either technique. The last, embedding-while-dithering, technique has been designed for palette images obtained from true color images using color quantization and dithering. In this technique, both the color quantization error and the error due to message embedding are diffused through the image to avoid introducing artifacts inconsistent with the dithering algorithm.

A hybrid watermark for tamper detection in digital images

A new hybrid image authentication watermark obtained as a combination of a fragile and a robust watermark is presented. The fragile watermark has good localization and security properties but cannot be used to distinguish malicious changes, such as feature adding or removal, from innocent image processing operations. The hybrid watermark can be used to accurately pinpoint changes as well as distinguish malicious tamper from innocent operations. The authentication can be done without accessing any information about the original image. Examples of tamper detection on real imagery are given. Powerful publicly available image processing software packages such as Adobe PhotoShop or PaintShop Pro make digital forgeries a reality. Feathered cropping enables replacing or adding features without causing detectable edges. It is also possible to carefully cut out portions of several images and combine them together while leaving barely detectable traces. Thus, the classical forensic techniques are not readily applicable to digital imagery.

Robust Digital Watermarking Based on Key-Dependent Basis Functions

In this paper, we introduce the concept of key-dependent basis functions and discuss its applications to secure robust watermarking for copyright protection and to designing secure public black-box watermark detectors. The new schemes overcome a possible security weakness of global, non-adaptive schemes that apply watermark patterns spanned by a small number of publicly known basis functions. The watermark is embedded into the projections of an image onto the secret set of key-dependent functions (patterns). The robustness of the watermarking scheme with respect to filtering, lossy compression, and combinations of many other attacks is studied. Finally, we propose a candidate for a watermarking scheme that enables the construction of a secure public watermark detector.

Discrete-time dynamical system under observational uncertainty

Abstract Discrete-time dynamical systems under observational uncertainty are studied. As a result of the uncertainty, points on an orbit are surrounded by uncertainty sets. The problem of reconstructing the original orbit given the sequence of uncertainty sets is investigated. The key property which makes the reconstruction possible is the sensitivity to initial conditions. A general reconstructing algorithm is theoretically analyzed and experimentally tested on several low-dimensional systems. The technique is extended to coupled one-dimensional maps with the goal of eventually developing retrospective techniques for partial differential equations exhibiting spatio-temporal chaos. Provided the coupling strength remains small and the coupling term has bounded first derivatives, it is conjectured that for dynamical systems with a positive Liapunov exponent the observational uncertainty can be reduced exponentially with the length of the orbit used for reconstruction. Computer experiments with the coupled logistic map are consistent with this conjecture.